Slope Deflection Method
All structures must satisfy:
1. Load-displacement relationship
2. Equilibrium of forces
3. Compatibility of displacements
Using the principle of superposition by considering separately the
moments developed at each support of a typical prismatic beam (AB)
shown in Fig. 1(a) of a continuous beam, due to each of the displacements
, θA, θB, and ∆ , and the applied loads. Assume clockwise moments are
+ive.
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The slope deflection equations (1 or 2) relate the unknown moments
applied to the nodes to the displacements of the nodes for
any span of the structure.
To summarize application of the slope-deflection equations, consider the
continuous beam shown in Fig. (2) which has four degrees of freedom.
Now equation (2) can be applied to each of the three spans.
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Problems
Analyze the structures shown, then draw the shearing force and bending
moment diagrams.
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